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The Structure of Models of Peano Arithmetic
Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard …
Cardinal Arithmetic
Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically …
A Study of Logics
It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to …
Groups of Finite Morley Rank
The book is devoted to the theory of groups of finite Morley rank. These groups arise in model theory and generalize the concept of algebraic groups over algebraically closed …
Sketches of an Elephant: A Topos Theory Compendium
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas …
Models of Peano Arithmetic
Nonstandard models of arithmetic are of interest to mathematicians through the presence of infinite (or nonstandard) integers and the various properties they inherit from the …
Change, Choice and Inference
Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The …
Many-Valued Logics
The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those …
Geometric Stability Theory
This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine …
Arithmetic, Proof Theory, and Computational Complexity
This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of …
Sketches of an Elephant: A Topos Theory Compendium
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas …
Labelled Deductive Systems
This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas by the notion of structured families …